How many people have ever celebrated a birthday where their age matches the current POTUS number?

What is the maximum number of times that someone has been able to match their age with the POTUS number?

Has there ever been a sitting president who matched their POTUS number in this way?

I will define this metric — the number of times that your age matches the number of the current president as the POTUS Number Number (PNN). Here are some observations about PNNs that try to answer the above questions:

PNN = 1

PNN = 2

People who turned one year old at any point in the last year of George Washington's presidency would — assuming they continued to live — have then been two years old during some stage of the presidency of POTUS #2. These people would therefore be the first to experience matching their POTUS number twice, i.e. gaining a PNN of 2. More generally, anyone who celebrates gaining their first PNN point in the last year of a presidency, has a good chance of gaining a second PNN point. For example, barring any bizarre gardening accidents, I will be 45 when POTUS #45 takes office on January 20, 2017. This will increment my PNN from 1 to 2.

Inaugurations: a bonus day for PNN seekers

Presidential inaugurations mark the handover of power between two presidents on a single day. Over the course of history, presidential inaugurations have happened on five different calendar dates. Before the Twentieth Amendment to the United States Constitution, inaugurations mostly took place on March 4, but since then they mostly take place on January 20. Some exceptions have been when the inauguration would fall on a Sunday, in which case it is pushed back one day.

This means, that March 4 and January 20 have probably been the days on which the most PNN points have been awarded. For example, the 2009 inauguration (on January 20) meant that that people who were turning 43 or 44 on that day could both gain a PNN point.

PNN > 2?

For a chance of advancing beyond a PNN of 2, someone would need a sitting president to serve a shorter than usual term. The president in question would also have to depart office within a year of assuming the presidency.

POTUS #9 died in office after just one month. This means that someone who turned 8 years old between March 4 and April 4, 1840 (PNN = 1) would have turned 9 during POTUS #9's ill-fated tenure in 1841 (PNN = 2), and would then have turned 10 while POTUS #10 was still in office (PNN = 3).

POTUS #20 is the only other president to serve for less than a year, and as he passed away in 1881, it means that there is no-one alive today who can still be a member of the very exclusive 'PNN = 3' club.

FDR: the scourge of PNN 2 seekers

Since the passing of the Twenty-second Amendment to the Constitution, presidents can only serve two terms in office, limiting a president to four or eight years in office (the latter occurring when a president seeks, and secures, re-election).

This amendment was introduced after the death of POTUS #32 who served as president for over 12 years. As you have the best chance of securing a 2nd PNN point if you achieve your first PNN point in the penultimate year of a presidency, FDR's long rule meant that it decreased the options for 32 year olds seeking an additional PNN point.

POTUS PNN?

Now we can turn to the important question of whether any sitting president ever achieved a PNN. As we are currently at POTUS #44, you might think this would be unlikely…and you would be correct. There have only been two presidents who took office when they were younger than 44. POTUS #26 was 42 and POTUS #35 was 43.

The closest we have come to this situation is with the current POTUS (#44), who was 47 when he took office, giving us a PNN differential of 3. POTUS #42 was the next closest with a PNN differential of 4 (he took office at the age of 46).

However, as the POTUS number continues to increase, we will surely see a sitting president gain a PNN in the near future. It could happen as soon as 2017 as there are three candidates seeking to secure the Republican Party nomination who are all aged 44 (Ted Cruz, Marco Rubio, and Bobby Jindal). However, Ted Cruz will be 45 on December 22, 2015; this means that — should he be elected President — he will miss the chance of gaining a POTUS PNN by just under a month.
Given Bobby Jindal's recent polling numbers, only Marco Rubio has any sort of realistic chance of becoming POTUS #45 at age 45 (with the added benefit of joining the PNN=2 club).

No end to PNNs?

Obviously there were no PNNs to be gained before America elected their first president. This made me wonder whether one day the POTUS number will get so high that no-one will be able to gain any new PNN points, i.e. when POTUS number > average life expectancy.

The average term of office since the inauguration of POTUS #34 in 1953 is about 6 years. So we can forecast that by the year 2100, we may see the election of POTUS #59 (assuming that term limits do not change and that America, and its presidential system of government, endures).

Life expectancy will surely increase over that period as well. The average American born today has a life expectancy of about 79 years. This is just a little higher than the age of POTUS #40 when he became the oldest president to leave office at the age of 77. The UN's World Population Prospects report predicts that by 2100, average life expectancy of Americans might rise to about 88 or 91 (male and female respectively).

Based on these numbers it seens that there will be plenty of PNNs to be gained in the foreseeable future. My two-year old son may have to wait until the year 2064 or so though before he can gain his first PNN, when POTUS #53 will be in office.